i listened to your explanation of what might have happened when patricia’s husband moved their lexus in the driveway (starter not engaging, smoke, etc.), and I thought you might have missed a few clues that she gave you. this is from show 1312 (featuring Martha stewart).
the first question I would have asked was “did he start the car before moving it?”. from her description, i’d say the answer was “no”, but I hate assuming that. the reason it might be relevant is because it’s normal for a car to have zero braking power if the engine isn’t running, and if the driveway is not level, he may have stopped the car by putting it into ‘Park’. I don’t know anything about lexus automobiles, but I do know that some engines and electronic systems have a peculiar relationship with the transmission (think “Saab”), and perhaps that could have caused the starter solenoid failure, etc.